Dynamical Tides Research Articles

The Measurement of Dynamic Tidal Contribution to Apsidal Motion in Heartbeat Star KIC 4544587

Abstract Apsidal motion is a gradual shift in the position of periastron. The impact of dynamic tides on apsidal motion has long been debated, because the contribution could not be quantified due to the lack of high-quality observations. KIC 4544587 with tidally excited oscillations has been observed by Kepler high-precision photometric data based on long-time-baseline and short-cadence schema. In this paper, we compute the rate of apsidal motion that arises from the dynamic tides as 19.05 ± 1.70 mrad yr−1 via tracking the orbital phase shifts of tidally excited oscillations. We also calculate the procession rate of the orbit due to the Newtonian and general relativistic contribution as 21.49 ± 2.8 and 2.4 ± 0.06 mrad yr−1, respectively. The sum of these three factors is in excellent agreement with the total observational rate of apsidal motion 42.97 ± 0.18 mrad yr−1 measured by eclipse timing variations. The tidal effect accounts for about 44% of the overall observed apsidal motion and is comparable to that of the Newtonian term. Dynamic tides have a significant contribution to the apsidal motion. The analysis method mentioned in this paper presents an alternative approach to measuring the contribution of the dynamic tides quantitatively.

The key impact of the host star’s rotational history on the evolution of TOI-849b

Context. TOI-849b is one of the few planets populating the hot-Neptune desert and it is the densest Neptune-sized one discovered so far. Its extraordinary proximity to the host star, together with the absence of a massive H/He envelope on top of the 40.8 M⊕ rocky core, calls into question the role played by the host star in the evolution of the system. Aims. We aim to study the impact of the host star’s rotational history on the evolution of TOI-849b, particularly focussing on the planetary migration due to dynamical tides dissipated in the stellar convective envelope, and on the high-energy stellar emission. Methods. Rotating stellar models of TOI-849 are coupled to our orbital evolution code to study the evolution of the planetary orbit. The evolution of the planetary atmosphere is studied by means of the JADE code, which uses realistic X-ray and extreme-ultraviolet (XUV) fluxes provided by our rotating stellar models. Results. Assuming that the planet was at its present-day position (ain = 0.01598 AU) at the protoplanetary disc dispersal, with mass 40.8 M⊕, and considering a broad range of host star initial surface rotation rates (Ωin ∈ [3.2, 18] Ω⊙), we find that only for Ωin ≤ 5 Ω⊙ do we reproduce the current position of the planet, given that for Ωin > 5 Ω⊙ its orbit is efficiently deflected by dynamical tides within the first ∼40 Myr of evolution. We also simulated the evolution of the orbit for values of ain ≠ 0.01598 AU for each of the considered rotational histories, confirming that the only combination suited to reproduce the current position of the planet is given by ain = 0.01598 AU and Ωin ≤ 5 Ω⊙. We tested the impact of increasing the initial mass of the planet on the efficiency of tides, finding that a higher initial mass (Min = 1 MJup) does not change the results reported above. Based on these results we computed the evolution of the planetary atmospheres with the JADE code for a large range of initial masses above a core mass of 40.8 M⊕, finding that the strong XUV-flux received by the planet is able to remove the entirety of the envelope within the first 50 Myr, even if it formed as a Jupiter-mass planet.

Star-planet interactions

Context. Tidal interactions and planetary evaporation processes impact the evolution of close-in star–planet systems. Aims. We study the impact of stellar rotation on these processes. Methods. We compute the time evolution of star–planet systems consisting of a planet with an initial mass between 0.02 and 2.5 MJup (6 and 800 MEarth) in a quasi-circular orbit with an initial orbital distance between 0.01 and 0.10 au, around a solar-type star evolving from the pre-main-sequence (PMS) phase until the end of the main-sequence phase. We account for the evolution of: the stellar structure, the stellar angular momentum due to tides and magnetic braking, the tidal interactions (equilibrium and dynamical tides in stellar convective zones), the mass evaporation of the planet, and the secular evolution of the planetary orbit. We consider that at the beginning of the evolution, the proto-planetary disk has fully dissipated and planet formation is complete. Results. We find that both a rapid initial stellar rotation and a more efficient angular momentum transport inside the star, in general, contribute to the enlargement of the domain that is devoid of planets after the PMS phase, in the plane of planet mass versus orbital distance. Comparisons with the observed distribution of exoplanets orbiting solar mass stars, in the plane of planet mass versus orbital distance (addressing the “Neptunian desert” feature), show an encouraging agreement with the present simulations, especially since no attempts have been made to fine-tune the initial parameters of the models to fit the observations. We also obtain an upper limit for the orbital period of bare-core planets that agrees with observations of the “radius valley” feature in the plane of planetary radius versus the orbital period. Conclusions. The two effects, namely, tides and planetary evaporation, should be accounted for simultaneously and in a consistent way, with a detailed model for the evolution of the star.

Revisiting Kepler-444

Context.Kepler-444 is one of the oldest planetary systems known thus far. Its peculiar configuration consisting of five sub-Earth-sized planets orbiting the companion to a binary stellar system makes its early history puzzling. Moreover, observations of HI-Lyαvariations raise many questions about the potential presence of escaping atmospheres today.Aims.We aim to study the orbital evolution of Kepler-444-d and Kepler-444-e and the impact of atmospheric evaporation on Kepler-444-e.Methods.Rotating stellar models of Kepler-444-A were computed with the Geneva stellar evolution code and coupled to an orbital evolution code, accounting for the effects of dynamical, equilibrium tides and atmospheric evaporation. The impacts of multiple stellar rotational histories and X-ray and extreme ultraviolet (XUV) luminosity evolutionary tracks are explored.Results.Using detailed rotating stellar models able to reproduce the rotation rate of Kepler-444-A, we find that its observed rotation rate is perfectly in line with what is expected for this old K0-type star, indicating that there is no reason for it to be exceptionally active as would be required to explain the observed HI-Lyαvariations from a stellar origin. We show that given the low planetary mass (~0.03 M⊕) and relatively large orbital distance (~0.06 AU) of Kepler-444-d and e, dynamical tides negligibly affect their orbits, regardless of the stellar rotational history considered. We point out instead how remarkable the impact is of the stellar rotational history on the estimation of the lifetime mass loss for Kepler-444-e. We show that, even in the case of an extremely slow rotating star, it seems unlikely that such a planet could retain a fraction of the initial water-ice content if we assume that it formed with a Ganymede-like composition.

Asteroseismology of Close Binary Stars: Tides and Mass Transfer

The study of stellar oscillations allows us to infer the properties of stellar interiors. Meanwhile, fundamental parameters such as mass and radius can be obtained by studying stars in binary systems. The synergy between binarity and asteroseismology can constrain the parameter space of stellar properties and facilitate the asteroseismic inference. On the other hand, binarity also introduces additional complexities such tides and mass transfer. From an observational perspective, we briefly review the recent advances in the study of tidal effects on stellar oscillations, focusing on upper main sequence stars (F-, A-, or OB- type). The effect can be roughly divided into two categories. The first one concerns the tidally excited oscillations (TEOs) in eccentric binaries where TEOs are mostly due to resonances between dynamical tides and gravity modes of the star. TEOs appear as orbital-harmonic oscillations on top of the eccentric ellipsoidal light curve variations (the 'heartbeat' feature). The second category is regarding the self-excited oscillations perturbed by static tides in circularized and synchronized close binaries. It includes the tidal deformation of the propagation cavity and its effect on eigenfrequencies, eigenfunctions, and the pulsation alignment. We list binary systems that show these two types of tidal effect and summarise the orbital and pulsation observables. We also discuss the theoretical approaches used to model these tidal oscillations and relevant complications such as non-linear mode coupling and resonance locking. Further information can be extracted from the observations of these oscillations which will improve our understanding of tides. We also discuss the effect of mass transfer, the extreme result of tides, on stellar oscillations. We bring to the readers' attention: 1) oscillating stars undergoing mass accretion (A-, F-, and OB type pulsators and white dwarfs), for which the pulsation properties may be changed significantly by accretion; 2) post-mass transfer pulsators, which have undergone a stable or unstable Roche-Lobe overflow. These pulsators have great potential in probing detailed physical processes in stellar interiors and mass transfer, as well as in studying the binary star populations.

Asteroseismology of Close Binary Stars: Tides and Mass Transfer

The study of stellar oscillations allows us to infer the properties of stellar interiors. Meanwhile, fundamental parameters such as mass and radius can be obtained by studying stars in binary systems. The synergy between binarity and asteroseismology can constrain the parameter space of stellar properties and facilitate the asteroseismic inference. On the other hand, binarity also introduces additional complexities such tides and mass transfer. From an observational perspective, we briefly review the recent advances in the study of tidal effects on stellar oscillations, focusing on upper main sequence stars (F-, A-, or OB- type). The effect can be roughly divided into two categories. The first one concerns the tidally excited oscillations (TEOs) in eccentric binaries where TEOs are mostly due to resonances between dynamical tides and gravity modes of the star. TEOs appear as orbital-harmonic oscillations on top of the eccentric ellipsoidal light curve variations (the “heartbeat” feature). The second category is regarding the self-excited oscillations perturbed by static tides in circularized and synchronized close binaries. It includes the tidal deformation of the propagation cavity and its effect on eigenfrequencies, eigenfunctions, and the pulsation alignment. We list binary systems that show these two types of tidal effect and summarize the orbital and pulsation observables. We also discuss the theoretical approaches used to model these tidal oscillations and relevant complications such as non-linear mode coupling and resonance locking. Further information can be extracted from the observations of these oscillations which will improve our understanding of tides. We also discuss the effect of mass transfer, the extreme result of tides, on stellar oscillations. We bring to the readers' attention: (1) oscillating stars undergoing mass accretion (A-, F-, and OB type pulsators and white dwarfs), for which the pulsation properties may be changed significantly by accretion; (2) post-mass transfer pulsators, which have undergone a stable or unstable Roche-Lobe overflow. These pulsators have great potential in probing detailed physical processes in stellar interiors and mass transfer, as well as in studying the binary star populations.

Dynamical tide in stellar radiative zones. General formalism and evolution for low-mass stars

Context. Most exoplanets detected so far are close-in planets, which are likely to be affected by tidal dissipation in their host star. To obtain a complete picture of the evolution of star–planet systems, we need to consider the effect of tides within stellar radiative and convective zones. Aims. We aim to provide a general formalism allowing us to assess tidal dissipation in stellar radiative zones for late- and early-type stars, including stellar structure with a convective core and an envelope like in F-type stars. This allows us to study the dynamics of a given system throughout the stellar evolution. On this basis, we investigate the effect of stellar structure and evolution on tidal dissipation in the radiative core of low-mass stars. Methods. We developed a general theoretical formalism to evaluate tidal dissipation in stellar radiative zones that is applicable to early- and late-type stars. From the study of adiabatic oscillations throughout the star, we computed the energy flux transported by progressive internal gravity waves and the induced tidal torque. By relying on grids of stellar models, we studied the effect of stellar structure and evolution on the tidal dissipation of F-, G-, and K-type stars from the pre-main sequence (PMS) to the red giant branch (RGB). Results. For a given star–planet system, tidal dissipation reaches a maximum value on the PMS for all stellar masses. On the main sequence (MS), it decreases to become almost constant. The dissipation is then several orders of magnitude smaller for F-type than for G- and K-type stars. During the subgiant phase and the RGB, tidal dissipation increases by several orders of magnitude, along with the expansion of the stellar envelope. We show that the dissipation of the dynamical tide in the convective zone dominates the evolution of the system during most of the PMS and the beginning of the MS, as the star rotates rapidly. Tidal dissipation in the radiative zone then becomes the strongest contribution during the subgiant phase and the RGB as the density at the convective-radiative interface increases. For similar reasons, we also find that the dissipation of a metal-poor star is stronger than the dissipation of a metal-rich star during the PMS, the subgiant phase, and the RGB. The opposite trend is observed during the MS. Finally, we show that the contribution of a convective core for the most massive solar-type stars is negligible compared to that of the envelope because the mass distribution of the core does not favor the dissipation of tidal gravity waves.

Temperature and Distance Dependence of Tidal Circularization in Close Binaries: A Catalog of Eclipsing Binaries in the Southern Hemisphere Observed by the TESS Satellite

Abstract Tidal forces are important for understanding how close binary stars and compact exoplanetary systems form and evolve. However, tides are difficult to model, and significant uncertainties exist about the strength of tides. Here, we investigate tidal circularization in close binaries using a large sample of well-characterized eclipsing systems. We searched TESS photometry from the southern hemisphere for eclipsing binaries. We derive best-fit orbital and stellar parameters by jointly modeling light curves and spectral energy distributions. To determine the eccentricity distribution of eclipsing binaries over a wide range of stellar temperatures (3000–50,000 K) and orbital separations a/R 1 (2–300), we combine our newly obtained TESS sample with eclipsing binaries observed from the ground and by the Kepler mission. We find a clear dependency of stellar temperature and orbital separation in the eccentricities of close binaries. We compare our observations with predictions of the equilibrium and dynamical tides. We find that while cool binaries agree with the predictions of the equilibrium tide, a large fraction of binaries with temperatures between 6250 K and 10,000 K and orbital separations between a/R 1 ∼ 4 and 10 are found on circular orbits, contrary to the predictions of the dynamical tide. This suggests that some binaries with radiative envelopes may be tidally circularized significantly more efficiently than usually assumed. Our findings on orbital circularization have important implications also in the context of hot Jupiters, where tides have been invoked to explain the observed difference in the spin–orbit alignment between hot and cool host stars.

Dynamical Tides in Jupiter as Revealed by Juno

Abstract The Juno orbiter has continued to collect data on Jupiter's gravity field with unprecedented precision since 2016, recently reporting a nonhydrostatic component in the tidal response of the planet. At the mid-mission perijove 17, Juno registered a Love number k 2 = 0.565 ± 0.006 that is −4% ± 1% (1σ) from the theoretical hydrostatic k 2 ( hs ) = 0.590 . Here we assess whether the aforementioned departure of tides from hydrostatic equilibrium represents the neglected gravitational contribution of dynamical tides. We employ perturbation theory and simple tidal models to calculate a fractional dynamical correction Δk 2 to the well-known hydrostatic k 2. Exploiting the analytical simplicity of a toy uniform-density model, we show how the Coriolis acceleration motivates the negative sign in the Δk 2 observed by Juno. By simplifying Jupiter’s interior into a coreless, fully convective, and chemically homogeneous body, we calculate Δk 2 in a model following an n = 1 polytrope equation of state. Our numerical results for the n = 1 polytrope qualitatively follow the behavior of the uniform-density model, mostly because the main component of the tidal flow is similar in each case. Our results indicate that the gravitational effect of the Io-induced dynamical tide leads to Δk 2 = − 4% ± 1%, in agreement with the nonhydrostatic component reported by Juno. Consequently, our results suggest that Juno obtained the first unambiguous detection of the gravitational effect of dynamical tides in a gas giant planet. These results facilitate a future interpretation of Juno tidal gravity data with the purpose of elucidating the existence of a dilute core in Jupiter.

Dynamical tides in neutron stars: the impact of the crust

ABSTRACT We consider the dynamical tidal response of a neutron star in an inspiralling binary, focussing on the impact of the star’s elastic crust. Within the context of Newtonian gravity, we add the elastic aspects to the theoretical formulation of the problem and quantify the dynamical excitation of different classes of oscillation modes. The results demonstrate the expectation that the fundamental mode dominates the tidal response and show how the usual tidal deformability (and the Love number) emerge in the static limit. In addition, we consider to what extent the different modes may be excited to a level where the breaking strain of the crust would be exceeded (locally). The results show that the fundamental mode may fracture the crust during the late stages of inspiral. This is also the case for the first gravity mode, which reaches the breaking threshold in strongly stratified stars. In our models with a fluid ocean, interface modes associated with the crust-ocean transition may also induce crust fracture. If this happens, it does so earlier in the inspiral, at a lower orbital frequency.

Detecting resonant tidal excitations of Rossby modes in coalescing neutron-star binaries with third-generation gravitational-wave detectors

Rossby modes ($r$-modes) of rotating neutron stars can be excited by the gravitomagnetic forces in coalescing binary systems. A previous study by Flanagan and Racine [Phys. Rev. D 75, 044001 (2007)] showed that this kind of dynamical tide (DT) can induce phase shifts of $\ensuremath{\sim}0.1\text{ }\text{ }\mathrm{rad}$ on gravitational waveforms, which is detectable by third-generation (3G) detectors. We study the impact of this DT on measuring neutron-star parameters in the era of 3G detectors. We incorporate two universal relations among neutron-star properties predicted by different equations of state: (i) the well-known I-Love relation between momentum of inertia and ($f$-mode) tidal Love number, and (ii) a relation between the $r$-mode overlap and tidal Love number, which we newly explore. We find that $r$-mode DT will provide rich information about slowly rotating neutron stars with frequency 10--100 Hz and spin inclination angle 18\ifmmode^\circ\else\textdegree\fi{}--110\ifmmode^\circ\else\textdegree\fi{}. For a binary neutron-star system (with a signal-to-noise ratio $\ensuremath{\sim}1500$ in the Cosmic Explorer), the spin frequency of each individual neutron star can be constrained to 6% (fractional error) in the best-case scenario. The degeneracy between the Love numbers of individual neutron stars is dramatically reduced: each individual Love number can be constrained to around 20% in the best case, while the fractional error for both symmetric and antisymmetric Love numbers are reduced by factors of around 300. Furthermore, DT also allows us to measure the spin inclination angles of the neutron stars, to 0.09 rad in the best case, and thus place constraints on neutron-star natal kicks and supernova explosion models. In addition to parameter estimation, we also develop a semianalytic method that accurately describes detailed features of the binary evolution that arise due to the DT.

Probing hybrid stars with gravitational waves via interfacial modes

One of the uncertainties in nuclear physics is whether a phase transition between hadronic nuclear matter to quark matter exists in supranuclear matter equations of state. Such a feature can be probed via gravitational-wave signals from binary neutron star inspirals that contain information of the induced tides. The dynamical part of the tides is caused by the resonance of pulsation modes of stars, which causes a shift in the gravitational-wave phase. In this paper, we investigate the dynamical tides of the interfacial mode ($i$-mode) of spherical degree $l=2$, a non-radial mode caused by an interface associated with a quark-hadron phase transition inside a hybrid star. In particular, we focus on hybrid stars with a crystalline quark matter core and a fluid hadronic envelope. We find that the resonant frequency of such $i$-modes typically ranges from 300Hz to 1500Hz, and the frequency increases as the shear modulus of the quark core increases. We next estimate the detectability of such a mode with existing and future gravitational-wave events from the inspiral waveform with a Fisher analysis. We find that GW170817 and GW190425 have the potential to detect the $i$-mode if the quark-hadron phase transition occurs at sufficiently low pressure and the shear modulus of the quark matter phase is large enough. We also find that the third-generation gravitational-wave detectors can further probe the $i$-mode with intermediate transition pressure. This finding opens a new, interesting direction for probing the existence of quark core inside a neutron star.

Relativistic effective action of dynamical gravitomagnetic tides for slowly rotating neutron stars

Gravitomagnetic quasi-normal modes of neutron stars are resonantly excited by tidal effects during a binary inspiral, leading to a potentially measurable effect in the gravitational-wave signal. We take an important step towards incorporating these effects in waveform models by developing a relativistic effective action for the gravitomagnetic dynamics that clarifies a number of subtleties. Working in the slow-rotation limit, we first consider the post-Newtonian approximation and explicitly derive the effective action from the equations of motion. We demonstrate that this formulation opens a way to compute mode frequencies, yields insights into the relevant matter variables, and elucidates the role of a shift symmetry of the fluid properties under a displacement of the gravitomagnetic mode amplitudes. We then construct a fully relativistic action based on the symmetries and a power counting scheme. This action involves four coupling coefficients that depend on the internal structure of the neutron star and characterize the key matter parameters imprinted in the gravitational waves. We show that, after fixing one of the coefficients by normalization, the other three directly involve the two kinds of gravitomagnetic Love numbers (static and irrotational), and the mode frequencies. We discuss several interesting features and dynamical consequences of this action, and analyze the frequency-domain response function (the frequency-dependent ratio between the induced flux quadrupole and the external gravitomagnetic field), and a corresponding Love operator representing the time-domain response. Our results provide the foundation for deriving precision predictions of gravitomagnetic effects, and the nuclear physics they encode, for gravitational-wave astronomy.

The phenomenology of dynamical neutron star tides

ABSTRACT We introduce a phenomenological, physically motivated, model for the effective tidal deformability of a neutron star, adding the frequency dependence (associated with the star’s fundamental mode of oscillation) that comes into play during the late stages of the binary inspiral. Testing the model against alternative descriptions, we demonstrate that it provides an accurate representation of the dynamical tide up to close to merger. The simplicity of the prescription makes it an attractive alternative for a gravitational-wave data analysis implementation, facilitating an inexpensive construction of a large number of templates covering the relevant parameter space.

Tidally excited oscillations in hot white dwarfs

ABSTRACT We study the flux variation in helium white dwarfs (WDs) induced by dynamical tides for a variety of WD models with effective temperatures ranging from $T=10\, {\rm kK}$ to $T=26\, {\rm kK}$. At linear order, we find the dynamical tide can significantly perturb the observed flux in hot WDs. If the temperature $T\gtrsim 14\, {\rm kK}$, then the dynamical tide may induce a fractional change in the flux by $\gt 1{{\ \rm per\ cent}}$ when the orbital period is $P_{\rm orb}\simeq 20{\!-\!}60\, {\rm min}$. The ratio between the flux modulation due to the dynamical tide and that due to the equilibrium tide (i.e. ellipsoidal variability) increases as the WD’s radius decreases, and it could exceed $\mathcal {O}(10)$ if the WD has a radius R ≲ 0.03 R⊙. Unlike the ellipsoidal variability which is in phase with the orbital motion, the pulsation caused by the dynamical tide may have a substantial phase shift. A cold WD with $T\simeq 10\, {\rm kK}$, on the other hand, is unlikely to show observable pulsations due to the dynamical tide. At shorter orbital periods, the dynamical tide may break and become highly non-linear. We approximate this regime by treating the waves as one-way travelling waves and find the flux variation is typically reduced to 0.1–1 per cent and the excess phase is ∼90° (though with large uncertainty). Even in the travelling-wave limit, the flux perturbation due to dynamical tide could still exceed the ellipsoidal variability for compact WDs with R ≲ 0.02 R⊙. We further estimate the non-linear flux perturbations oscillating at four times the orbital frequency dominated by a self-coupled parent g-mode driving low-order daughter p modes. The non-linear flux variation could be nearly $50{{\ \rm per\ cent}}$ of the linear variation for very hot WD models with $T\gtrsim 26\, {\rm kK}$ and $1{{\ \rm per\ cent}}$ linear flux variation. We thus predict that both the linear and non-linear flux variations due to dynamical tides are likely to have significant observational signatures.

On the Evolution of the Globular Cluster System in NGC 1052-DF2: Dynamical Friction, Globular–Globular Interactions, and Galactic Tides

Abstract The ultradiffuse galaxy NGC 1052-DF2 has an overabundance of luminous globular clusters (GCs), and its kinematics is consistent with the presence of little to no dark matter. As the velocity dispersion among the GCs is comparable to the expected internal dispersions of the individual GCs, the galaxy might be highly conducive to GC–GC merging. If true, this could explain the puzzling luminosity function of its GCs. Here we examine this possibility by resimulating three of our earlier simulations of the GC system, where the GCs were modeled as single particles, with live GCs. Somewhat surprisingly, we infer a low merger rate of ∼0.03 Gyr−1. The main reason is that the GCs are too dense for tidal shock capture, caused by impulsive encounters among them, to operate efficiently (we infer a tidal capture rate of only ∼0.002 Gyr−1). Therefore, whatever mergers occur are driven by other mechanisms, which we find to be captures induced by dynamical friction and compressive tides from other GCs. The low merger rate inferred here makes it unlikely that the unusually large luminosities of the GCs can be explained as a result of past GC–GC mergers. Our simulations also indicate that, if NGC 1052-DF2 is indeed largely devoid of dark matter, its tidal field is too weak to induce any significant mass loss from the GCs. Therefore, in such a scenario, we predict that it is improbable for the GCs to reveal tidal features, something that can be tested with future deep observations.

Gravitational waveforms of binary neutron star inspirals using post-Newtonian tidal splicing

The tidal deformations of neutron stars within an inspiraling compact binary alter the orbital dynamics, imprinting a signature on the gravitational wave signal. Modeling this signal could be done with numerical-relativity simulations, but these are too computationally expensive for many applications. Analytic post-Newtonian treatments are limited by unknown higher-order nontidal terms. This paper further builds upon the "tidal splicing" model in which post-Newtonian tidal terms are "spliced" onto numerical relativity simulations of black-hole binaries. We improve on previous treatments of tidal splicing by including spherical harmonic modes beyond the (2,2) mode, expanding the post-Newtonian expressions for tidal effects to 2.5 order, including dynamical tide corrections, and adding a partial treatment of the spin-tidal dynamics. Furthermore, instead of numerical relativity simulations, we use the spin-aligned binary black hole (BBH) surrogate model "NRHybSur3dq8" to provide the BBH waveforms that are input into the tidal slicing procedure. This allows us to construct spin-aligned, inspiraling TaylorT2 and TaylorT4 splicing waveform models that can be evaluated quickly. These models are tested against existing binary neutron star and black hole-neutron star simulations. We implement the TaylorT2 splicing model as an extension to "NRHybSur3dq8," creating a model that we call "NRHybSur3dq8Tidal."

Non-linear dynamical tides in white dwarf binaries

ABSTRACT Compact white dwarf (WD) binaries are important sources for space-based gravitational-wave (GW) observatories, and an increasing number of them are being identified by surveys like Extremely Low Mass (ELM) and Zwicky Transient Facility (ZTF). We study the effects of non-linear dynamical tides in such binaries. We focus on the global three-mode parametric instability and show that it has a much lower threshold energy than the local wave-breaking condition studied previously. By integrating networks of coupled modes, we calculate the tidal dissipation rate as a function of orbital period. We construct phenomenological models that match these numerical results and use them to evaluate the spin and luminosity evolution of a WD binary. While in linear theory the WD’s spin frequency can lock to the orbital frequency, we find that such a lock cannot be maintained when non-linear effects are taken into account. Instead, as the orbit decays, the spin and orbit go in and out of synchronization. Each time they go out of synchronization, there is a brief but significant dip in the tidal heating rate. While most WDs in compact binaries should have luminosities that are similar to previous traveling-wave estimates, a few per cent should be about 10 times dimmer because they reside in heating rate dips. This offers a potential explanation for the low luminosity of the CO WD in J0651. Lastly, we consider the impact of tides on the GW signal and show that the Laser Interferometer Space Antenna (LISA) and TianGO can constrain the WD’s moment of inertia to better than $1{{\ \rm per\ cent}}$ for centi-Hz systems.

Excitation of f -modes during mergers of spinning binary neutron star

Tidal effects have important imprints on gravitational waves (GWs) emitted during the final stage of the coalescence of binaries that involve neutron stars (NSs). Dynamical tides can be significant when NS oscillations become resonant with orbital motion; understanding this process is important for accurately modeling GW emission from these binaries, and for extracting NS information from GW data. In this paper, we carry out a systematic study on the tidal excitation of fundamental modes of spinning NSs in coalescencing binaries, focusing on the case when the NS spin is anti-aligned with the orbital angular momentum-where the tidal resonance is most likely to take place. We first expand NS oscillations into stellar eigen-modes, and then obtain a Hamiltonian that governs the tidally coupled orbit-mode evolution. We next find a new approximation that can lead to analytic expressions of tidal excitations to a high accuracy, and are valid in all regimes of the binary evolution: adiabatic, resonant, and post-resonance. Using the method of osculating orbits, we obtain semi-analytic approximations to the orbital evolution and GW emission; their agreements with numerical results give us confidence in on our understanding of the system's dynamics. In particular, we recover both the averaged post-resonance evolution, which differs from the pre-resonance point-particle orbit by shifts in orbital energy and angular momentum, as well as instantaneous perturbations driven by the tidal motion. Finally, we use the Fisher matrix technique to study the effect of dynamical tides on parameter estimation. We find that the dynamical tides may potentially provide an additional channel to study the physics of NSs. The method presented in this paper is generic and not restricted to f mode; it can also be applied to other types of tide.

Formation rate of LB-1-like systems through dynamical interactions

Abstract We estimate formation rates of LB-1-like systems through dynamical interactions in the framework of the theory of stellar evolution before the discovery of the LB-1 system. The LB-1 system contains a ∼70 ${M_{\odot}}$ black hole (BH), a so-called pair instability (PI) gap BH, and a B-type star with solar metallicity, and has nearly zero eccentricity. The most efficient formation mechanism is as follows. In an open cluster, a naked helium star (with ∼20 ${M_{\odot}}$) collides with a heavy main sequence star (with ∼50 ${M_{\odot}}$) which has a B-type companion. The collision results in a binary consisting of the collision product and the B-type star with a high eccentricity. The binary can be circularized through the dynamical tide with radiative damping of the collision product envelope. Finally, the collision product collapses to a PI-gap BH, avoiding pulsational pair instability and pair instability supernovae because its He core is as massive as the pre-colliding naked He star. We find that the number of LB-1-like systems in the Milky Way galaxy is ∼0.01(ρoc/104 ${M_{\odot}}$ pc−3), where ρoc is the initial mass densities of open clusters. If we take into account LB-1-like systems with O-type companion stars, the number increases to ∼0.03(ρoc/104 ${M_{\odot}}$ pc−3). This mechanism can form LB-1-like systems at least ten times more efficiently than the other mechanisms: captures of B-type stars by PI-gap BHs, stellar collisions between other types of stars, and stellar mergers in hierarchical triple systems. We conclude that no dynamical mechanism can explain the presence of the LB-1 system.